When I try to render, the camera renders from the wrong position
Check in the outliner to see if you have another camera in the scene.  The one that is shown in the Gif, doesn't have its triangle completely coloured in - it's just the outline of a triangle. If it's completely coloured in, it's the ACTIVE camera. With the visible camera you want to render from still selected, press Control and Number Pad 0.
That will throw you into the camera view of that camera and make it the active one.